1. Basics of Optical Interferometry (Observationnal Astronomy II) Lecture by Stéphane Sacuto

2. Power of Resolution and need for High Angular Resolution PSF  I Obj D Source with F s < l /D PSF The information on your object is lost. You NEED more spatial resolution from your instrument.

3. ObjectsWavelength (µm)Angular size (mas)Telescope diameter (m) Circumstellar envelope around o Ceti (M star) 115045 Volcanoes of Io (Jupiter satellite) 510100 Nucleus of NGC 1068 (AGN) 2.2< 1> 400 Spots on the photosphere of a Cen (Solar type) 0.50.071500 Typical monolithic telescope diameters Those structures are not resolved with monolithic telescopes even with the ELT We need something else INTERFEROMETRY

4. PSF D Source with F s < l /D The signal of the source is found again but under the appearance of fringes Interferometric signal D D B but F s ~ l /B < l /D

5. L3 L2 L1 Delay line and optical path compensation B B p =B.sin(z) z =B.cosz DL=L1

6. The interferometric signal PSF of the telescope Interferometric signal l/D l/B Fringe contrast is given by :  I max - I min I max + I min V An Interferometer is measuring the contrast of the total fringe pattern : FsFs +

7. The fringe contrast (part I) High contrast Mid contrastLow contrast V~1V~0.6V~0.2 Small source ( F s << l /B ) Mid source ( F s ~ l /B )Large source ( F s ~ l /D )  For a given baseline length B and for different sizes of the source F s

8.  For a given dimension of the source F s and for different baseline lengths B High contrast Mid contrastLow contrast V~1V~0.6V~0.2 Small base ( B << l / F s ) Mid base ( B ~ l / F s ) Large base ( B >> l / F s ) The fringe contrast (part II)

9. Object-Contrast Relation The Van Cittert and Zernike theorem ? V= | Ô ( u, v ) / Ô (0,0) |

10. The Van Cittert and Zernike theorem The fringe contrast of a source of emissivity O is equal to the modulus of the Fourier Transform of O at a given spatial frequency normalized by the FT of O at the origin. u v u v u v Fourier space/uv-plane/ spatial frequencies plane | Ô (u,v) / Ô ( 0,0 )| F Direct Space O (a,d) a d a d a d O (a,d). exp[- i.2p ( u a + v d)]. da dd òò O (a,d). da dd Does someone recognize this denominator?

11. Some Fourier (Hankel) transformations (*) r = (a² + d²) 1/2 (*) q = ( u ² + v ²) 1/2 = B p /l (**) J 1c (X) = J 1 (X)/X

12. Plane of the star BxBx ByBy B p =B=130 m PA T0T0 Plane of the star B p =100 m BxBx BYBY PA T1T1 After an Earth rotation The uv-plane (part I) spatial frequencies ( u, v ) : coordinates (B x,B y ) of the projected baselines (B p ) seen from the star and divided by the observing wavelength  ) u = B x /l = B p.cos(PA) / l v = B y /l = B p.sin(PA) / l PA Earth plane B p /l = Öu² + v²

13. after 1 hour of observation Wavelength dispersion (u=B x /l ; v=B y /l ) a d ?? a d u v = v u a d a d u v = v u after 6 hours a d ?? a d u = v u after 42 hours with 7 pairs v The uv-plane (part II) Observation of R Scl ( a =01:26:58 ; d =-32:32:35) at the date of 19 August 2011 This kind of coverage is very expensive in time ! F F -1 Observations

14. What is the appropriate uv coverage? It depends on the complexity of the object Is it really necessary to get a very large uv-coverage for such an object? [hot star] Is it necessary to get a very large uv-coverage for this one? [Post-AGB (triple system + envelope + disk)]

15.  Spatial information

16.  Spectral information B=60m (mid dusty region) B=90m (inner dusty region) B=120m (molecular region) 1R  2R  3R  4R  5R  6R  B=30m (outer dusty region) MgFeSiO 4 TiO 2 Al 2 O 3 Fe Mg 2 SiO 4 SiO 2 AmC H2OH2O SiC SiO TiO C2H2C2H2 HCN

17. The Phase in Interferometry: V = V e - i  00 Binary source at angle  0 => displacement of the fringes by OPD =  0.B B  0.B information on the asymmetries of an object  12 =  12 obj + d 2 – d 1 Van Cittert-Zernike theorem   u,v) = arg[ Ô  u,v  ] = atan [ Im( Ô )/Re( Ô) ] Atmospheric noise

18. The Closure Phase Observed Object Atmosphere  12 =  12 obj + d 2 – d 1  23 =  23 obj + d 3 – d 2  31 =  31 obj + d 1 – d 3  123 =  12 +  23 +  31 =  12 obj +  23 obj +  31 obj T1 T2 T3 Object Only!!

19. UD of 9 mas diameter with a spot of 2 mas diameter on its surface representing 25% of the total flux. Fringe contrast Closure Phase An Example UD UD+spot

20. Real visibility data points (AMBER with 3 telescopes)

21. Closure Phase data

22. Model vs Data (part I)

23. Model vs Data (part II) 2.17 µm continuum 2.38 µm CO-line 10 mas

24. The calibration in Interferometry

25. The need for accurate determination of the calibrator diameters Calibrated visibility where System response Unresolved calibrator Error on visibility solely due to uncertainty on the calibrator diameter Resolved calibrator

26. Effects of diameter uncertainties on the visibility accuracy  cal /  cal = 3%  cal /  cal = 1%

27. ASPRO The Astronomical Software to PRepare Observations

28. http://www.jmmc.fr/aspro_page.htm How to launch ASPRO in the web?

29. The interface – WHEN: to define the date and time of the simulated observation – WHERE: to select the interferometer (VLTI, IOTA, CHARA, …) and the number of telescopes – WHAT: to define the target properties (name, coordinates, brightness); – OBSERVABILITY/COVERAGE: to define the VLTI configuration to be used for the observations – MODEL/FIT: to calculate and plot interferometric observables and their associated uncertainties according to the chosen model (UD, LD, Binary, …) and the corresponding baseline configuration.

30. When

31. Where

32. What

33. Observability delay line Night UT time LST time

34. uv-coverage (part I)

35. uv-coverage (part II)

36. Model/Fit (part I)

37. Model/Fit (part II)

38. Model/Fit (part III)

39. Uniform diskResolved binaryUniform disk + Uniform ring Model/Fit (part IV) [F 1 /F 2 ] 10µm =4 s = 40mas q =45° Æ = 10mas Æ = 30mas [F 1 /F 2 ] 10µm =1 f ext = 40mas f in = 20mas Æ = 10mas BpBp V l=10µm V BpBp BpBp V D I R E C T F O U R I E R S P A C E

40. DEFINE THE BEST CALIBRATOR http://www.jmmc.fr/searchcal_page.htm How to launch SearchCal in the web?

41. CALIBRATORS  Choose your observing wavelength (AMBER-H/K or MIDI-N)  The maximum baseline of your observation (limit of sensitivity)  The science target  The maximum location around the science target (close enough to avoid atmospheric biases)  And get your calibrators (from the various catalogs existing)

42. Table  Separation from the science target in degree  Evaluation of the corresponding equivalent UD visibility value

43. Selection criteria  location of the calibrator (as close as possible)  brightness (as bright as possible to get a high Signal to Noise ratio)  spectral type and luminosity (avoid complex object like cool stars)  visibility and accuracy (avoid too large objects -> V small -> poor S/N ratio)  variability (avoid to use variable objects that may lead to temporal biases in the calibrated measurements)  multiplicity (avoid multiple object that may lead to a wrong interpretation of the calibrated measurements)

44. DEFINE THE BEST CALIBRATOR HD35497